Five-Full-Block Structured Singular Values of Real Matrices Equal Their Upper Bounds

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Abstract

We show that the structured singular value of a real matrix with respect to five full complex uncertainty blocks equals its convex upper bound. This is done by formulating the equality conditions as a feasibility SDP and invoking a result on the existence of a low-rank solution. A counterexample is given for the case of six uncertainty blocks. Known results are also revisited using the proposed approach.

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  • Control Engineering
Original languageEnglish
Pages (from-to)583 - 586
Number of pages4
JournalIEEE Control Systems Letters
Volume5
Issue number2
Publication statusPublished - 2021 Apr
Publication categoryResearch
Peer-reviewedYes